Monday, September 12, 2016

My solar panels were installed in August of last year, and two months later I reported on how they were performing. Now, after a full year of operation, it’s time for a more comprehensive report.

The bottom line is that the panels produced a little less electrical energy than the installer predicted, but still quite a bit more than I used over the course of the year. Here’s a diagram showing the overall energy flows:

Here and throughout this article I’ll present data from the year that began on 1 September 2015 and ended on 31 August 2016. During that time the panels produced 1558 kilowatt-hours (kWh) of electrical energy, and I used 349 kWh of that energy directly. The other 1209 kWh went onto the grid for my neighbors to use. But I also pulled 813 kWh of energy off the grid, at night and at other times when I needed more power than the panels were producing. My total home usage from both the panels and the grid was 1162 kWh. (I got the solar production amount from my Enphase solar monitoring system, and the amounts going to and from the grid by reading my electric meter. From these three numbers I calculated the other two.)

Because I used less energy than my panels produced, I’ve paid no usage charges on my electric bills since the system was installed; I pay only the monthly minimum charges, which come to about $9.00 per month including taxes. Under Utah’s net-metering policy (which could change in the future), each kWh that I push onto the grid can offset the cost of a kWh that I pull off of the grid at some other time. But I don’t get to make a profit from the 396 kWh excess that I pushed onto the grid over the course of the year; that was effectively a donation to Rocky Mountain Power, worth about $40 at retail rates.

Monthly and daily details

So much for the yearly totals. But the picture varies quite a bit with the seasons, as shown in this graph of my panels’ monthly output:

The total energy generated in July (165 kWh) was twice as much as in January (81 kWh), with a pretty steady seasonal rise and fall in between. On the other hand, my installer estimated significantly higher production in winter and spring, plotted on the graph as green squares. (I get a similar over-estimate of the winter and spring production, relative to summer and fall, when I use the NREL PVWatts calculator, with weather data from the Ogden airport. So maybe my location is cloudier than the airport, and/or maybe last winter was cloudier than the 30-year average that the calculator uses.) The actual annual production of 1558 kWh was 91% of the estimated total of 1713 kWh. (An earlier, less formal estimate from the installer was 1657 kWh for the year, and not broken down by month; my annual production was 94% of that estimate.)

You might think the factor-of-2 seasonal variation in my solar energy production was a direct result of the varying length of the days and/or the varying solar angles. In fact, however, it was mostly due to varying amounts of cloud cover. You can see this in a plot of the daily energy generated:

The energy output on sunny days varied only a little with the seasons, and was actually lowest in the summer. But summer days in northern Utah are consistently sunny, whereas a full day of sunshine can be uncommon in mid-winter. Incidentally, my best day of all was February 23 (6.7 kWh), while my worst day was January 30 (0.0 kWh, because it snowed throughout the day).

Although the seasonal variations among sunny days are relatively small, they’re still interesting. The output drops off in mid-winter because the days are shorter, and also because the mountains block the early morning sunlight. On the other hand, the output drops off in the summer because of the steep angle of my roof. The panels face the noon sun almost directly throughout the fall and winter, but they face about 37 degrees too low for the mid-summer noon sun, reducing the amount of solar power they receive by about 20% (because the cosine of 37° is 0.8). The following plot shows all these effects:

Notice that the vertical axis on this plot is power, or the rate of energy production. To get the total energy generated you need to multiply the power by the time elapsed, which is equivalent to calculating the area under the graph. As you can see, the June graph is lowest at mid-day but extends farther into the early morning and late afternoon, while the December graph is highest but narrowest. The total energy (area) is largest for the March graph. The asymmetry in the December graph, and in the lowest part of the March graph, is from the mountains blocking the rising sun. The smooth “shoulders” on either side come from the shadow of the pointy gable in the middle of my roof.

With all of these effects in mind, as well as the day-to-day variations in cloud cover, let me now show all of my solar data for the year in a single image. Here the day of the year is plotted from top to bottom, and the time of day from left to right. The power level in watts is represented by color, with brighter colors indicating higher power levels:

In the upper-left portion of this image you can more or less see the shape of the mountains, with a reflection at the winter solstice. The dark stripes are cloudy days, with the exception of a power outage during the wind storm of May 1 (that’s right—a standard grid-connected photovoltaic system produces no power when the grid goes out). Subtle astronomical effects cause some further asymmetries from which, with enough analysis, you could probably extract the shape of the analemma.

Details aside, the big picture is that the steepness of my roof is almost ideal for the winter months. It even ensures that snow slides off the panels as soon as the sun comes out. But the steep angle hurts my solar production more in the summer than it helps in the winter, mostly because so many winter days are cloudy anyway.

Effect of temperature

Looking back at the previous graph for the three sunny days in different seasons, you might have noticed that the noon power level drops from winter to summer by more than the 20% predicted by the solar geometry. The discrepancy on any particular day could be due to variable amounts of haze, but there’s another important effect: temperature.

To isolate the effect of temperature, I took the noon power level for every day of the year and divided it by the (approximate) cosine-theta geometrical factor to get what the power would have been if the panels were directly facing the sun. Then I plotted this adjusted power level vs. the ambient temperature (obtained from Ogden-area weather reports) to get the following graph:

The data points cluster along a line or curve with a negative slope, confirming that the panels produce less power at higher temperatures. Very roughly, it appears that the power output is about 15% less at 90°F than at 20°F. For comparison, the data sheet for the solar panels indicates that the power should drop by 0.43% for each temperature increase of 1 degree Celsius, or about 17% for an increase of 70°F. But this specification is in terms of the temperature of the panels, which I wouldn’t expect to vary by the same amount as the ambient temperature.

(In the preceding plot, the outlying data points below the cluster are from days when clouds reduced the solar intensity; most such points lie below the range shown in the graph. I’m pretty sure that the outliers above the cluster are from partly cloudy days when the panels were getting both direct sunlight and some reflected light from nearby clouds.)

Electricity usage

Now let’s look at the seasonal variation in my home electricity usage, compared to the solar panels’ output. Here’s a graph of the monthly data, with the solar data now plotted as blue squares and the usage plotted as columns, divided into direct-from-solar usage and from-the-grid usage:

Unfortunately, my electrical usage peaks in mid-winter, when the solar production is at a minimum! But even during the bulk of the year when the solar production exceeds my total use, well over half of the electricity I use comes off the grid, not off the panels.

The good news is that I’ve actually reduced my total electricity use by about 15% since the panels were installed. I did this through several small changes: running the furnace less when I was away from home; cooling my house in the summer with a super-efficient whole house fan instead of smaller fans sitting in windows; and unplugging an old computer and a portable “boom box” stereo that were drawing a few watts even when turned off. I’m still using more electricity than I did a decade ago, when I had no home internet service and no hard-wired smoke detectors. But if you look just at what I’m using off the grid, it’s slightly lower even than back in those simpler times. Here’s an updated plot of my average daily usage during every month since I bought my house 18 years ago (as explained more fully in this article from last year):

What would it take to live off the grid?

I’ve repeatedly emphasized the electrical energy that I continue to draw from the grid, because I want readers to understand that virtually all of the solar panels being installed these days are part of the electrical grid—not an alternative to it. Even though my panels generate more electrical energy than I use over the course of a year, they will not function without a grid connection and of course they generate no power at all during most of the times when I need it.

But what would it take to live off the grid entirely? The most common approach is to combine an array of solar panels with a bank of batteries, which store energy for later use when the sun isn’t shining. For example, there’s been a lot of talk recently about the new Tesla Powerwall battery, which stores 6.4 kWh of energy—enough to power my home for about two days of average use. A Tesla Powerwall sells for $3000, which is somewhat more than the net cost (after tax credits) of my solar panels. If I were to make that further investment, could I cut the cord and live off the grid?

To answer this question, I combined my daily solar generation data with a data set of nightly readings of my electric meter. (The latter data set is imperfect due to inconsistent reading times, missed readings when I was away, and round-off errors, but day-to-day errors cancel out over longer time periods so it should give the right picture overall.) I then calculated what the charge level of my hypothetical Tesla Powerwall would be at around sunset on each day, and plotted the result:

For most of the year the battery would hold more than enough energy to get through the nights, but in this simulation there were 42 evenings in the late fall and winter when the level dropped to zero, and several more evenings when it dropped low enough that it would surely be empty by morning. Simply getting a Tesla Powerwall is not enough to enable me, or most other households with solar panels, to disconnect from the grid.

What if I added a second Tesla battery? Unfortunately, that would reduce the number of zero-charge nights by only eight, from 42 to 34. In fact, it would take thirteen Tesla batteries, in this simulation, to completely eliminate zero-charge nights, because there is a period of a few weeks during mid-winter when the average output of my solar panels is barely over half what I’m using.

The better solution, therefore, would be to add more solar panels. For example, if I were to double the size of my solar array and install two Tesla Powerwalls, then the simulation predicts that I would run out of electricity just one night during the year. Of course this scenario is still extremely wasteful, because I’d be using less than half the capacity of the panels and only a small fraction of the capacity of the batteries during most of the year. That’s why people who actually live off the grid tend to have backup generators that run on chemical fuels, and don’t rely on electricity for most of their heating or cooking.

Similar calculations would apply to our society as a whole. A massive investment in both solar panels and batteries could conceivably get us to the point where most of our electricity, for most of the year, is coming from the sun. But it will never be economical to get that “most” up to 100%, because so much over-building would be needed to get through periods of cloudy weather, and it will be much less expensive to use other energy sources at those times.